Direct 3D mapping of the Fermi surface and Fermi velocity

• Published in: Nature materials 2017-06, Vol.16 (6), p.615-621
• Main Authors: Medjanik, K., Fedchenko, O., Chernov, S., Kutnyakhov, D., Ellguth, M., Oelsner, A., Schönhense, B., Peixoto, T. R. F., Lutz, P., Min, C.-H., Reinert, F., Däster, S., Acremann, Y., Viefhaus, J., Wurth, W., Elmers, H. J., Schönhense, G.
• Format: Article
• Language: English
• Subjects: 140/146; 639/766/119; 639/766/119/995; Band structure of solids; BCC metals; Binding energy; Biomaterials; Body centered cubic lattice; Brillouin zones; Condensed Matter Physics; Data recording; Electron conductivity; Electron spin; Electronic structure; Energy gap; Mapping; Materials Science; Nanotechnology; Optical and Electronic Materials; Photoelectric emission; Soft x rays; Surface chemistry; Three dimensional imaging; Tungsten; Velocity; Velocity distribution
• ISSN: 1476-1122; 1476-4660
• DOI: 10.1038/nmat4875

We performed a full mapping of the bulk electronic structure including the Fermi surface and Fermi-velocity distribution v F ( k F ) of tungsten. The 4D spectral function ρ ( E B ; k ) in the entire bulk Brillouin zone and 6 eV binding-energy ( E B ) interval was acquired in ∼3 h thanks to a new multidimensional photoemission data-recording technique (combining full-field k -microscopy with time-of-flight parallel energy recording) and the high brilliance of the soft X-rays used. A direct comparison of bulk and surface spectral functions (taken at low photon energies) reveals a time-reversal-invariant surface state in a local bandgap in the (110)-projected bulk band structure. The surface state connects hole and electron pockets that would otherwise be separated by an indirect local bandgap. We confirmed its Dirac-like spin texture by spin-filtered momentum imaging. The measured 4D data array enables extraction of the 3D dispersion of all bands, all energy isosurfaces, electron velocities, hole or electron conductivity, effective mass and inner potential by simple algorithms without approximations. The high-Z bcc metals with large spin–orbit-induced bandgaps are discussed as candidates for topologically non-trivial surface states. Time-of-flight momentum microscopy is developed. It enables direct three-dimensional mapping of the topology of the Fermi surface, identification of electron and hole pockets, and quantification of Fermi velocity as a function of wavevector.